What are your thoughts on truely elliptical planforms?

Any thoughts on truly elliptical planforms... Vortices moving inboard, reduced fidelity in airfoil due to construction techniques, aileron effectiveness, etc..

Red, nice to hear from you again!

As someone with recent experience building a reasonably elliptical wing (the wing for our Supermarine Spitfire Mk.22 quarter-40 pylon racer), I can tell you that elliptical wings are easier; easier to mess up the airfoils while making the plug, easier to make a mistake in design, easier to get ripples in your mylar if you try to bag them, easier to develop difficult to spot alignment problems, easier to thoroughly destroy any anticipated schedule for development,...

So why do people bother with them? Supposedly to improve the lift distribution and reduce "induced" drag. Induced drag is the drag that comes as a natural (and inevitable) by-product of producing lift with a wing of less than infinite span. Traditional wing theory holds that generally speaking, an aircraft with an elliptical lift distribution along its span will have the lowest induced drag.

There are exceptions to this, including (among other things) aircraft with winglets, situations involving interactions between various parts of the aircraft,etc.. It also refers to the net lift distribution of the entire aircraft, including the fuselage and tail surfaces, although the common (but not always valid) approach is to ignore those and concentrate on just the wing.

Note I said elliptical spanwise lift distribution, NOT elliptical wing. There are many ways to get an elliptical lift distribution from a wide variety of planforms, twists and airfoil combinations. The problem with most of them is that they usually have an elliptical lift distribution at only one flight condition.

For example, I could design a constant chord wing (sometimes called a "Hershey bar" wing because its shape resembles the chocolate confection by that name), with a constant airfoil shape but a non-linear washout distribution that would give it a perfect elliptical lift distribution at thermalling conditions. The problem is that as soon as the angle of attack changed, the lift distribution wouldn't be elliptical anymore. In fact, at low lift, high speed conditions (such as penetrating, or at launch for a HLG) the tips could actually be producing negative lift, with extra positive lift demanded from the center section to compensate! Not good at all.

Another approach might be to use flaps and drooping ailerons to approximate an elliptical lift distribution at a variety of flight conditions by altering the effective washout with the flap/aileron mix. This is a practical solution with today's computer radios, but it requires some fairly good analysis capabilities to determine the correct mixing schedule, and some very good rigging and flying techniques to achieve it. Not impossible, and definitely easier to design than a good non-flapped wing, but still challenging.

In the case of our Spitfire wing, we used the natural deflections of the wing as it deflected under almost 20 G's load on the pylon turns to alter the twist by about 1 degree, so that the lift distribution was elliptical on the straights AND on the turns. If we hadn't, the model would have had negative lift on the tips (causing high drag) on the straights, or else a poor lift distribution and possible tip stall problems on the turns. By the way, this sort of aeroelastic tailoring usually requires finite element stress analysis (which fortunately we have!).

Here's where the elliptical planform starts to look attractive. Theoretically, a truly elliptical planform, with a constant airfoil section and zero washout, will have a constant lift coefficient along the entire span of the wing, and an elliptical lift distribution AT ALL ANGLES OF ATTACK!

Sounds almost too good to be true, right? Well it is. The key word here is "theoretically". The key assumption in that is that there will be no change in airfoil characteristics with changes in chord, that the hopelessly small tip airfoil will behave the same as the big wide root chord does at a Reynolds number several times higher. While this MIGHT be an ALMOST valid assumption at full scale Reynolds numbers, at model airplane Reynolds numbers this is almost never valid. At typical model sailplane Reynolds numbers, the behavior of the small tip airfoil will be quite different from the root airfoil, leading to serious tip stall tendencies and a non-elliptical lift distribution at many flight conditions. You could of course use washout and airfoil variations along the span to compensate, but at that point it isn't a non-twisted, constant airfoil, constant spanwise lift coefficient elliptical wing anymore!

The exception might be some of the faster racing classes. For example, the Reynolds numbers of a Quarter-40 class pylon model at high speed on the race course are in the same general region as a lot of general aviation full scale aircraft. At the higher Reynolds numbers the variations due to Reynolds numbers are somewhat less significant, making the concept workable. Even so, some airfoil tailoring (like what we used on the Spitfire) is usually necessary to provide some tip stall margin.

There is evidence that rounded tips (such as a truly elliptical wing's) encourage the airflow to pull inward toward the root at the trailing edge, dragging the tip vortices with them and reducing the effective span, which increases induced drag. Straight trailing edges, winglets and crescent wing planforms or sheared (swept back) tips are all ways to combat this. Of course if you use any of those you might still have an elliptical chord distribution but it won't be a truly elliptical wing anymore.

A historical note:
What is probably the most famous example of the elliptical planform, the Supermarine Spitfire, was NOT built that way for purely aerodynamic reasons. The aircraft was originally sketched with a conventional tapered wing, but a later revision to the design specification added some extra machine guns in the wing. The thickness of the tapered wing where these extra guns would be was insufficient to enclose them. Rather than adding blsiters or increasing the airfoil % thickness (which would hurt the critical Mach number and high speed characteristics), R.J. Mitchell used the modified (not truly) elliptical planform to increase the chord in the area of the extra guns enough to enclose them, without changing the airfoil shape.

As far as aileron effectiveness goes, other than the well known tendency for constant-airfoil rounded or elliptical tips to have tip stall problems, control authority seems to be otherwise acceptable in most cases. The elliptical chord distribution does help keep mass in the tips to a minimum, which usually helps stability and control in both roll and yaw.

Then of course there's the issue of how to build it. A built up structure with no sheeting is actually not to bad to build once you get all the ribs designed and cut out. Our Chrysalis wing, although not elliptical, faces many of the same challenges as a truly elliptical wing, and we recommend it for beginners. It was a huge amount of work to design, and each rib is distinctly different from all the others, so each had to be drawn individually. No short cuts were possible. Still, once I had the files ready for the laser, it was no different than any other wing, and it does fly very well. Like I said though, it isn't an elliptical wing.

A sheeted elliptical wing is much harder to build because you're trying to form flat wood around a 3-dimensional curved shape. Wood sheets don't like to do that. Neither does Mylar, so if you try to do a foam core/glass skin wing you're likely to have ripples in it when it comes out of the bag. Then there's the problem of how to cut the core. One method involves warping the foam core block into an elliptical dihedral shape, cutting the upper airfoil surface and then warping it the other way to cut the lower surface. It's very difficult to control the airfoil shapes and chords in the middle of the wing using this method. Another way is to cut a series of trapezoid shaped wing segments (we used 4 for each wing panel on the Spitfire), join them together and sand them to the final elliptical shape using more templates to control the airfoil shapes. Don't forget to stretch the chord lengths and the airfoil shapes at the ends of the segments when you're cutting them so that you end up with the correct airfoil shape all along the wing when you're done. Properly done this involves a huge amount of very precise hand work and at least twice as many templates as usual to get the finished wing. This may be acceptable for a one-off scratch-built, or to make the plug for a mold for a hollow-molded wing (what we were doing), but trying to mass produce a foam core by this method is a quick route to Chapter 11. Don't forget, even after you've made the core you still have to skin it somehow, and you're likely to have ripples in the finished part because of the 3-d curvature.

Overall, the theoretical advantages of the un-twisted constant airfoil elliptical wing are difficult to achieve in practice, particularly in models. By the time you fix the problems, it isn't elliptical, un-twisted or constant airfoil anymore. When I design a wing I simply develop the design that works best, taking all parameters and flight conditions collectively into account, and let the chips fall where they may. The result usually isn't even close to elliptical in the pure sense, although it may superficially resemble one.

One of the few cases where it makes sense to make the planform truly elliptical is if you're building an exact scale model of a full scale aircraft that used that planform (and note that even the full scale Spitfire isn't truly elliptical). Even then you'll probably have to take some liberties on the airfoils and twist if you want it to behave well in flight. Other than this special case, there are usually better choices for most wing designs than the ellipse.

Don Stackhouse
DJ Aerotech